Abbas appoints new Palestinian PM
Former Finance Minister Salam Fayyad, an independent, has been asked to take over and form an emergency government.
The move comes amid political upheaval in Gaza, where Hamas has forcibly taken control from its Fatah rivals.
But Ismail Haniya, of Hamas, said he was still prime minister, calling his government's dismissal "hasty".
A former World Bank executive, Fayyad is a well-respected figure internationally.
In recent months, foreign governments have chosen to deal with him directly as a means of bypassing Hamas, but Hamas has already rejected the appointment, saying it views the entire interim administration as illegal.
"It is a coup against legitimacy and a transgression of all the laws," Hamas spokesman Sami Abu Zuhri told the AFP news agency.
The group of Middle East mediators known as the Quartet - the U.S., UN, EU and Russia - pledged their "full support" for Abbas, a spokeswoman for EU foreign policy chief Javier Solana, said.
An uneasy calm has returned to the Strip after a week of fierce fighting between members of Abbas's Fatah movement and Hamas, which claimed at least 100 lives.
Vehicles returned to the roads and shops were open in Gaza. Few armed men were visible on the streets and there were reports of only sporadic gunfire.
As Hamas consolidated its grip on power, the group said it had released several top Fatah military commanders seized during the violence under a prisoner "amnesty".
Meanwhile, incidents of looting at former Fatah strongholds were reported, while the home of Fatah strongman Mohammed Dahlan was stripped bare.
Masked Hamas gunmen ransacked Abbas' seafront offices on Friday, discarding portraits of the Palestinian Authority President and his predecessor, Yasser Arafat, on the floor, their glass frames in pieces.
Elsewhere in Gaza, two Fatah men were killed, one of whom was thrown from a rooftop, the Associated Press news agency reported.
Meanwhile, Egyptian police said that 97 senior Fatah officials had fled from Gaza into Egypt overnight aboard a fishing boat.
About 100 other Fatah security workers have already sought refuge in Egypt.
A further 3,000 Palestinian civilians are now stranded on the Egyptian side of the Rafah crossing which is closed. Rafah provides the people of Gaza with their only point of access to the outside world.
Hamas has said it intends to take control of the crossing point. However, it is not certain that Israel, Egypt and the European monitors who operated the facility will allow that.
President Abbas dismissed the three-month-old unity government on Thursday and declared a state of emergency.
He has said he will rule by presidential decree until the conditions are right for early elections.
Under the Palestinian Basic Law, essentially the Palestinian constitution, the president can rule by decree for 30 days. This can be extended with the approval of the parliament.
The BBC's Matthew Price in Beit-ul-Moqaddas (Jerusalem) says this may be an irrelevance, as Abbas appears to no longer have any influence in Gaza.
Our correspondent says the West Bank and Gaza Strip will now effectively be split from one another - Gaza run by Hamas and the West Bank by Fatah.
There are also fears that violence will spread to the West Bank, where Fatah is dominant.